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M-SC in Mathematics at Shri Vishwakarma Skill University
Palwal, Haryana
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About the Specialization
What is Mathematics at Shri Vishwakarma Skill University Palwal?
This M.Sc. Mathematics program at Shri Vishwakarma Skill University focuses on equipping students with advanced theoretical knowledge and practical skills in various branches of mathematics. It emphasizes a blend of core mathematical concepts, computational techniques, and problem-solving methodologies, preparing graduates for diverse roles in academia, research, and industry. The program addresses the growing demand for skilled mathematicians in India''''s technology and data-driven sectors.
Who Should Apply?
This program is ideal for fresh graduates holding a B.Sc./B.A. with Mathematics, seeking to deepen their understanding of advanced mathematical concepts. It also caters to individuals aiming for research careers or those looking to apply sophisticated mathematical tools in analytics, finance, and engineering domains. Aspiring educators and working professionals in related fields who wish to upskill or transition into more specialized mathematical roles will find the curriculum beneficial.
Why Choose This Course?
Graduates of this program can expect to pursue career paths such as data scientists, quantitative analysts, research associates, or academicians in India. Entry-level salaries typically range from INR 4-7 LPA, with experienced professionals earning upwards of INR 10-15 LPA in analytical and research roles. The program provides a strong foundation for pursuing M.Phil. or Ph.D. degrees, contributing to India''''s scientific and technological advancements.
Student Success Practices
Foundation Stage
Build Strong Conceptual Foundations- (Semester 1-2)
Dedicate significant time to understanding the core theorems, proofs, and definitions in Abstract Algebra, Real Analysis, and Topology. Regularly solve problems from textbooks and online resources to solidify understanding and develop rigorous mathematical thinking.
Tools & Resources
NPTEL lectures, Rudin for Analysis, Dummit & Foote for Algebra, Munkres for Topology, Brilliant.org
Career Connection
A strong theoretical base is crucial for advanced research, competitive exams, and applying complex algorithms in data science or quantitative finance.
Develop Programming and Computational Skills- (Semester 1-2)
Actively engage with the Computer Programming (C/Python) practicals. Go beyond syllabus requirements by working on mini-projects, participating in coding challenges, and learning to implement mathematical algorithms.
Tools & Resources
HackerRank, LeetCode, Project Euler, Online Python/C tutorials
Career Connection
Essential for roles in computational mathematics, data analytics, scientific computing, and algorithmic development in tech companies.
Participate in Peer Learning and Study Groups- (Semester 1-2)
Form study groups with peers to discuss challenging concepts, collaborate on problem-solving, and prepare for examinations. Explaining concepts to others reinforces your own understanding and exposes you to different perspectives.
Tools & Resources
University library, Virtual meeting tools for group discussions
Career Connection
Enhances communication, teamwork, and collaborative problem-solving skills, highly valued in research teams and corporate environments.
Intermediate Stage
Deepen Specialization Through Electives and Projects- (Semester 3)
Carefully choose electives like Operations Research or Computer Graphics based on career interests. For Dissertation Part-I, identify a research area, conduct an extensive literature review, and formulate a clear problem statement.
Tools & Resources
Research journals (e.g., JSTOR), Academic databases, LaTeX, Software for Operations Research (e.g., Gurobi, PuLP) or Computer Graphics (e.g., OpenGL)
Career Connection
This stage helps in developing niche expertise, which is critical for specialized roles in analytics, research, or software development.
Seek Internship Opportunities- (Semester 3)
Actively look for summer or part-time internships in relevant industries like financial analytics, data science, or academic research labs. Internships provide invaluable real-world experience, exposure to industry challenges, and help build professional networks.
Tools & Resources
University career services, LinkedIn, Internshala.com, Company career pages
Career Connection
Internships are often a direct pathway to full-time employment and provide practical exposure that makes you job-ready for Indian companies.
Engage in Academic Competitions and Workshops- (Semester 3)
Participate in mathematical Olympiads, problem-solving competitions, or workshops on advanced topics like numerical methods or functional analysis. This hones problem-solving skills under pressure and broadens exposure to cutting-edge research.
Tools & Resources
Online competition platforms, University clubs, Professional mathematical societies
Career Connection
Builds a strong profile, demonstrates initiative and advanced problem-solving capabilities, highly regarded by recruiters and academic institutions.
Advanced Stage
Finalize Dissertation and Portfolio Development- (Semester 4)
Focus intensely on completing Dissertation Part-II, ensuring rigorous analysis, clear presentation of results, and adherence to academic standards. Concurrently, compile a portfolio of your projects, research work, and relevant coding assignments.
Tools & Resources
Academic writing guides, LaTeX, GitHub for code projects, Professional presentation software
Career Connection
A strong dissertation and a well-curated portfolio are crucial for securing research positions, academic roles, or advanced analytics jobs.
Intensive Placement Preparation and Networking- (Semester 4)
Begin intensive preparation for job interviews, focusing on quantitative aptitude, logical reasoning, and technical knowledge in your specialized areas. Network with alumni, attend career fairs, and connect with industry professionals.
Tools & Resources
Mock interview platforms, Online aptitude tests, LinkedIn, University placement cell
Career Connection
Directly improves chances of securing good placements in desired companies within India, including startups, MNCs, and research institutions.
Explore Higher Studies and Research Opportunities- (Semester 4 and beyond)
If aiming for an M.Phil. or Ph.D., research potential supervisors and universities. Prepare for entrance exams like NET/JRF or university-specific tests. Continuously read research papers in your field of interest to stay updated with the latest advancements.
Tools & Resources
UGC NET/JRF preparation materials, University prospectuses, Research databases (e.g., arXiv)
Career Connection
Opens doors to careers in pure research, academia, or advanced R&D roles in scientific and educational institutions across India and globally.
Program Structure and Curriculum
Eligibility:
- B.Sc./B.A. (Hons.) in Mathematics or B.Sc./B.A. with Mathematics as one of the subjects with 50% marks (45% for SC/ST/PwD candidates) or equivalent grade from a recognized University.
Duration: 4 semesters / 2 years
Credits: 80 Credits
Assessment: Internal: 30% (for theory papers), External: 70% (for theory papers)
Semester-wise Curriculum Table
Semester 1
| Subject Code | Subject Name | Subject Type | Credits | Key Topics |
|---|---|---|---|---|
| MS-C-101 | Abstract Algebra | Core | 4 | Groups, Subgroups, Normal Subgroups, Homomorphism, Permutation Groups, Sylow''''s Theorems, Rings, Integral Domains, Fields |
| MS-C-102 | Real Analysis | Core | 4 | Metric Spaces, Compactness, Connectedness, Sequences and Series of Functions, Riemann-Stieltjes Integral, Functions of Several Variables |
| MS-C-103 | Differential Equations | Core | 4 | Linear Differential Equations, Exact Equations, Higher Order Linear Equations, Series Solutions, Laplace Transforms, Boundary Value Problems, Partial Differential Equations |
| MS-C-104 | Classical Mechanics | Core | 4 | Constraints, Generalized Coordinates, D''''Alembert''''s Principle, Lagrange''''s Equation, Hamilton''''s Principle, Conservation Laws, Central Force Problem, Rigid Body Dynamics |
| MS-C-105P | Viva-Voce | Practical | 4 | Oral examination covering Semester 1 theory concepts, Problem solving skills, Conceptual understanding, Application of mathematical principles |
Semester 2
| Subject Code | Subject Name | Subject Type | Credits | Key Topics |
|---|---|---|---|---|
| MS-C-201 | Linear Algebra | Core | 4 | Vector Spaces, Subspaces, Linear Transformations, Eigenvalues and Eigenvectors, Inner Product Spaces, Orthogonalization, Diagonalization, Canonical Forms |
| MS-C-202 | Complex Analysis | Core | 4 | Analytic Functions, Cauchy-Riemann Equations, Complex Integration, Cauchy''''s Theorem, Taylor and Laurent Series, Residues, Conformal Mappings |
| MS-C-203 | Topology | Core | 4 | Topological Spaces, Open and Closed Sets, Neighborhoods, Basis and Subbasis, Continuous Functions, Connectedness, Compactness, Separation Axioms |
| MS-C-204 | Fluid Dynamics | Core | 4 | Ideal Fluids, Equation of Continuity, Euler''''s Equation, Bernoulli''''s Theorem, Irrotational Motion, Vorticity, Viscous Fluids, Navier-Stokes Equations, Boundary Layer Theory |
| MS-C-205P | Computer Programming in C/Python | Practical | 4 | Programming fundamentals, Data types, Control structures, Functions, Arrays, Pointers, Object-Oriented Programming concepts, Algorithm implementation in C/Python |
Semester 3
| Subject Code | Subject Name | Subject Type | Credits | Key Topics |
|---|---|---|---|---|
| MS-C-301 | Functional Analysis | Core | 4 | Normed Linear Spaces, Banach Spaces, Hilbert Spaces, Bounded Linear Operators, Dual Spaces, Hahn-Banach Theorem, Uniform Boundedness Principle |
| MS-C-302 | Partial Differential Equations | Core | 4 | First Order PDEs, Charpit''''s Method, Higher Order Linear PDEs, Classification of PDEs, Wave Equation, Heat Equation, Laplace Equation, Green''''s Functions |
| MS-E-301 | Operation Research | Elective | 4 | Linear Programming, Simplex Method, Duality Theory, Transportation Problems, Assignment Problems, Game Theory, Queuing Theory, Inventory Control |
| MS-C-303P | Dissertation Part-I | Project | 4 | Research methodology, Literature review, Problem identification, Project proposal development, Data collection techniques, Preliminary analysis, Report writing |
| MS-E-302P | Computer Graphics | Elective (Practical) | 4 | Graphics hardware, Output primitives, 2D and 3D transformations, Clipping, Projections, Surface rendering, Animation, Visualization techniques |
Semester 4
| Subject Code | Subject Name | Subject Type | Credits | Key Topics |
|---|---|---|---|---|
| MS-C-401 | Differential Geometry | Core | 4 | Curves in R3, Arc Length, Curvature, Torsion, Serret-Frenet Formulas, Surfaces in R3, First and Second Fundamental Forms, Gauss and Weingarten Maps |
| MS-C-402 | Advanced Numerical Analysis | Core | 4 | Numerical solutions of ODEs and PDEs, Finite Difference Methods, Finite Element Methods, Iterative methods for linear systems, Eigenvalue problems, Approximation theory |
| MS-C-403P | Dissertation Part-II | Project | 4 | Advanced research implementation, Data analysis and interpretation, Result formulation, Thesis writing, Presentation skills, Defense preparation, Publication ethics |
| MS-E-401 | Fuzzy Set Theory | Elective | 4 | Fuzzy sets, Membership functions, Fuzzy operations, Fuzzy relations, Fuzzy logic, Fuzzy systems, Fuzzy control, Applications in decision making |
| MS-E-402P | Graph Theory | Elective (Practical) | 4 | Graphs, Paths, Cycles, Trees, Connectivity, Planarity, Graph coloring, Matching, Network flows, Applications in computer science and operations research |
